Random matrix theory and robust covariance matrix estimation for financial data
摘要
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It is shown that the spectral estimator corresponds to an M-estimator proposed by Tyler (1983) in the context of elliptical distributions. Both the generalization of elliptical distributions and the development of a robust dispersion matrix estimator are motivated by the stylized facts of empirical finance. Random matrix theory is used for analyzing the linear dependence structure of high-dimensional data. It is shown that the Marcenko-Pastur law fails if the sample covariance matrix is considered as a random matrix in the context of elliptically distributed and heavy tailed data. But substituting the sample covariance matrix by the spectral estimator resolves the problem and the Marcenko-Pastur law remains valid.
引用
@article{arxiv.physics/0503007,
title = {Random matrix theory and robust covariance matrix estimation for financial data},
author = {Gabriel Frahm and Uwe Jaekel},
journal= {arXiv preprint arXiv:physics/0503007},
year = {2007}
}